Vague the question: how long have all the mathematicians working in the respective fields known the theory of categories?
More specific questions:
- Is it true that all modern working algebraic topologists know category theory? How long ago?
- Is it true that all modern working algebraists know category theory? How long ago?
Questions still remain somewhat vague. Of course, I am not interested in single exceptions. I got the impression that in many areas of modern mathematics the language of category theory (category, functor, limit, colimit, adjoint functor, etc.) is widely used in articles and therefore it is impossible to study this area without knowing the theory of categories. I'm wondering for which areas this is really true and for how long ago.